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comment Proving $\big(n!^{\frac1n}\big)_{n\in\mathbb N^*} \to \infty$
Makes sense, but that $a^{n−a}$ shouldn't be there, should it? I edited it out, feel free to rollback if needed. Also, you assume $a\in\mathbb N$, but that's without loss too; one just has to replace $a$ with $\lfloor a\rfloor$.
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suggested rejected edit on Proving $\big(n!^{\frac1n}\big)_{n\in\mathbb N^*} \to \infty$
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accepted Proving $\big(n!^{\frac1n}\big)_{n\in\mathbb N^*} \to \infty$
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revised Trouble with geometrical application of Lagrange multiplier
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